Data Structures, Algorithms, & Applications in C++
Chapter 10, Exercise 45

Yes, the compressed file produced by LZW compression can be longer than the original file. For example, consider a file with a single character. Since every code produced by the LZW compressor is 12 bits long, the single character file gets replaced by a 2 character file (the twelve-bit code gets output as two bytes in this case).

The worst that can happen is that each character of the input file is replaced by a twelve-bit code. So, if the input file is n bytes/characters long, the ``compressed file'' is at most ceil(1.5n) bytes long.